Going to the Moon requires more propellant than going to low Earth orbit NOT because the Moon is farther away but because the rocket must leave Earth at 41,000 km/h to reach the Moon while it needs only 30,000 km/h to reach low Earth orbit.

everybody knows that... but you're saying that, send an 1 mT payload to LEO or GEO or Moon or NEO or Mars or Jupiter or Saturn or Andromeda need the same amount of propellent... ...well, just reveal your secret to NASA and ESA so we can start a manned Mars mission next year... ...no need of dozens AresV and EDSs, no need of nuclear engines...

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It does not matter at all how close the asteroid comes to Earth. What matters is HOW FAST the asteroid is passing Earth.

as already said, the asteroids that run too fast will be (simply) not used

however, the asteroids' speed could be a problem to reach and rendezvous them near earth, but, when the payload is joined, it's an advantage, since, send the same payload, at the same speed to the same (billions km.) distance, in the same time, with chemical rokets, needs HUGE amounts of propellents and/or nuclear engines

however, I think that all options must be calculated on real payloads and real asteroids to know if it has small, big or no advantages

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But an asteroid has very weak gravity, and during the short time that it is close to the passing rocket its gravity will not be able to significantly alter the speed or direction of that rocket.

I don't suggest to use the asteroids' gravity for rockets' slingshot but as "taxi"

The only way to get the benefit of that asteroid's speed as it passes would be to physically grab it, or get in front of it and let it crash into your rocket as it passes that spot at high speed. And the speed would be many thousands of kilometers per hour.

He's got the answer to that - just don't use an asteroid that is going too fast!

Somehow I don't think spelling out every flaw is going to work, but I admire your patience.

Asteroids that pass Earth slowly are simply in orbits almost identical to Earth's orbit. They will never go far from Earth's orbit or anywhere near the orbit of another planet.

this is not a problem but an advantage for some missions

we need two kind of asteroids for exploration and as "space truck"

the "exploration asteroids" must have an orbit that goes over Pluto to explore objects we can't see with telescopes

the "space trucks" must have an orbit close to other planets

an asteroid that runs near Earth and Mars could be excellent to send soon big supply (oxygen, propelelnts, food, water, hardware, rovers, etc.) to Mars (parked on Phobos and Deimos) so, after 2030+, we must send ONLY the astronauts and a few hardware for very long Mars missions

an asteroid that runs near Earth and Mars could be excellent to send soon big supply (oxygen, propelelnts, food, water, hardware, rovers, etc.) to Mars

I calculate that an asteroid which comes close to both Earth and Mars will pass Earth at a speed of 10,601 km/hr. So to ride it to Mars your rocket needs to get to the place where the asteroid will pass and then speed up by 10,601 km/hr to softly land on it. But the space craft could just speed up by that same 10,601 km/hr with no asteroid there and go to Mars directly on its own. The presence of the asteroid does not help at all.

An asteroid that passes both Earth and Pluto will pass Earth at 42,529 km/hr. So to ride it to Pluto your rocket needs to get to the place where the asteroid will pass and then speed up by 42,529 km/hr to softly land on it. But the space craft could just speed up by that same 42,529 km/hr with no asteroid there and go to Pluto directly on its own. The presence of the asteroid does not help at all.

Any time the rocket speeds up by the required amount to land softly on the asteroid the rocket has placed itself in the same orbit around the Sun as that asteroid. It means the rocket will go wherever the asteroid would go even if it never lands on the asteroid.

The space craft always has to use just the same amount of propellant to land on the asteroid as it would to just go by itself wherever the asteroid was going to go.

. So to ride it to Mars your rocket needs to get to the place where the asteroid will pass and then speed up by 10,601 km/hr to softly land on it.

Who said anything about landing softly? We can construct a spacecraft that can survive impact with an asteroid at 10000 km/h and then mine and transport a large payload off that asteroid and bouncy-bouncy crashland on mars ;)

. So to ride it to Mars your rocket needs to get to the place where the asteroid will pass and then speed up by 10,601 km/hr to softly land on it.

Who said anything about landing softly? We can construct a spacecraft that can survive impact with an asteroid at 10000 km/h and then mine and transport a large payload off that asteroid and bouncy-bouncy crashland on mars

Oh, you had me going for a minute there. Well done!

A lasso and a really long bungee rope, and we could just swing from body to body. Call it Project Tarzan. No, that dates me - Project Spiderman!